Was Fisher (W)right?

Once again without internet, thundering my way north on the Silver Star. It is hard to keep focus on what I intended on the subject I am writing on. The Evolution meetings were inspiring to say the least. Lots of great talks, many of which I could easily write a blog about, but I must stay on phase one for the moment!

Like Barton and Charlesworth and Carson and Templeton , Fisher and Wright would have disagreed on the importance of genetic drift (That sentence must win some sort of prize for name dropping!). Fisher would have emphasized that small population size would decrease the number of alleles and the (molecular) genetic variation within populations. He also would have, in all likelihood, argued that most meaningful genetic variation was additive, and epistasis would not be present to any great extent. In contrast, Wright would have argued that gene interaction is important in populations, and as a result genetic drift could result in shifts in genetic architecture, and with that the potential to form what Dobzhansky called adaptive gene complexes.   What I want to talk about is that, much like the blind men examining the elephant, they could both be right.

Blind men elephant 2

In the classic fable of the blind men and the elephant each man examines only a part of the elephant, and fails to understand what the whole is.  (from http://www.newsfromthehill.com/2011/06/keep-on-sunny-side.html)

First, Fisher. If you have a population with a large amount of additive by additive epistasis and send it through a bottleneck you will find that the additive genetic variance increases (yea! That’s a big part of the reason I have tenure!). However, although the total genetic variance increases a little bit, the additive variance increases a lot more. The net result is that the epistatic variance declines precipitously. The net result is that after a few generations of small population size the epistatic genetic variance basically disappears. Selection will typically do the same thing. In general both drift and selection tend to drive genetic variance to lower levels. Thus dominance by dominance epistasis tends to be converted to additive by dominance, dominance, and additive variance. Similarly additive by additive variance tends to get converted to additive variance. It is because of this tendency that there is virtually no reason to bother with modeling or measuring three way and higher epistatic variance. It also means that most populations most of the time will also tend to have relatively little two locus epistatic variance. The bottom line: Fisher was right: Within populations under most circumstances we can ignore gene interactions, and treat populations as if they were additive. This means that in many cases genetic drift will simply have the effect of reducing the variance within populations.

epistasis and drift

After a few generations of small population size the nonadditive variance (green line minus red line) becomes very small. Fisher was right, within populations we can ignore gene interaction.

Importantly, however, this view that has Fisher as correct is focused within populations. Within populations the epistasis disappears as a variance component, but it does not go away. The interactions are still there, it is just that most of the time populations will be in a gene frequency space where most of the epistatic variance has been “converted” into additive variance. The other way that you can think of this is that the epistatic variance disappears it reappears as variance among populations. The way this happens conceptually is that when one of the loci gets fixed the epistatic interaction between a pair of loci will be converted into additive effect. Of course in reality, one allele doesn’t get fixed while the other stays at intermediate frequency, however, thinking simultaneously about both loci going to partial fixation tends to hurt my head.

So it is this between population component where Wright comes in. As I said the fixation of alleles leads to the conversion of epistasis to additive variance, however, in different populations it may be different alleles that get fixed by drift. Thus, in an interaction between the A and B locus it may be the B1 allele that moves towards fixation in one population and B2 that moves towards fixation in a second population. In both populations the additive variance will increase due to conversion of epistasis to additive variance, but the increased additive variance will be different in that different alleles at the A locus will be favored in the two populations. In other words, you don’t get something for nothing. An increase in additive genetic variance is always accompanied by a shift in what alleles do. I have mentioned this before and identified this as a shift in the local average effects of alleles. However, even without the fancy name it is an important effect. In interacting systems genetic drift has the potential to send a population down a new evolutionary trajectory. Although the mathematical tools to describe it were not available to him, I believe that this is what Wright was talking about when he was thinking about phase one of his shifting balance process.

Mixing of alleles

When there is epistasis genetic drift will not only increase the additive genetic variance, it will also change the average effects of alleles.    Thus, an allele that was “good” prior to a bottleneck may be “bad” after the bottleneck.

Thus, it appears that both Fisher and Wright were correct. Within populations genetics will typically act in an additive manner, and we will see that in many circumstances population bottlenecks will do little more than decrease the ability of a population to adapt. Thus, within populations a Fisherian view is expected to entirely adequate. However, that decrease might not be as much as you might expect (for what it is worth, the VA should increase whenever VAA > 1/3 VA – that is ignoring the typo in the relevant equation), and there may be some shifting of local average effects. This shift in the effects of alleles on the phenotype is what Wright was talking about. If we are looking at a metapopulation we need to acknowledge this effect of gene interactions on the differentiation of populations.

Just to remind you this shift of local average effects due to gene interactions is an entirely different form of population differentiation than differentiation of population means. Two populations with identical mean phenotypes can nevertheless be differentiated for average effects.

In conclusion, then we can see that indeed Fisher and Wright were looking at different parts of the same elephant. Fisher was looking at the apparently additive world that is within a population, and Wright was looking at the emphatically non-additive world that is between populations. I would argue that a modern enlightened view of phase one of Wright’s shifting balance theory would combine these two views. Within populations an additive view will typically be adequate. Genetic drift will as often as not lead to a decrease in additive genetic variance, and epistatic variance will typically not be detectable. The true effects of epistasis will primarily be seen among populations, and they will be seen in the form of shifts in local average effects. These are measures we typically do not make, so until we hve more data we will not know how important epistasis is in population differentiation.

Leave a Reply